Cnc Machining, Based On A Unified Mathematical Model Of Spiral Bevel Gear Tooth Surface

Spiral bevel gears are one of basic mechanical elements to transmit motion between concurrent or skew axes. They are widely applied to automobiles, tractors, airplane, mining machinery, machine tools and other mechanical products and they are one of the most important driving elements in equipment. They have quite a few merits, such as the big overlap ratio, the high loading capacity, the high transmitting efficiency, the stability, the small noises, and so on. In recent years, with the development of Free-Form-type CNC Spiral Bevel Gear Machine tools and extensive application, It is possible to process higher precision spiral bevel gears by more efficient and convenient method. But, the research of design and processing about spiral bevel gear at home and abroad is still based on traditional machine tool with cradle as a model, to vector computing and differential geometry as a tool, study the cutter and relative motion between cutter and bland; Therefore, spiral bevel gear can be divided into many forms in accordance with the different processing methods, the tooth surfaces got from different traditional processing methods are not the same, the focus on the study of CNC machining is only equivalent conversion the various traditional processing methods to CNC machine tools, not to develop a more advanced and simple gear design theory for CNC machine tools, so it can not be completely exploit the modernization processing capacity of CNC machine tool. So, it is very important to research the design of spiral bevel gear for NC machining .The digitization of the tooth face is an inevitable demand of design, manufacture, and measuring technology of the hypoid gear, the uniform mathematical model of the tooth surface is the basic condition of designing, manufacturing, and measuring integration. Because the advantages of NURBS surface at expression the products' geometric model, the NURBS surface has been released by ISO as the STEP standard of geometric definitions for industrial products, and regarded as the sole mathematical method of defining the shape of products. In view of this, the article is committed to spiral bevel gear tooth design, processing research based on the unit of tooth surface model by the use of NURBS surface.The tooth surfaces got from different traditional processing methods are not the same, but the traditional analytical model of the tooth surface can not tell the difference effectively and intuitively. In the use of NURBS method, we can obtain the unification expression of the various tooth surfaces, then, the geometry features can be obtained through calculation. Because of the significance of tooth surfaces curvature in the gear design and amendment, the focus of this article will be the curvature characteristics. First of all, analyze the curvature of different tooth surfaces and come up with a visual approach to distinguish various tooth surfaces; then, study about two pinions' curvature which process from different method and mate with the same bull wheel, probe the relationship between the tooth surfaces curvature and the imperfect contact pattern; finally, research the effects of different processing parameters on gear tooth surfaces curvature, come up with a new approach for the curvature's quantitative amended.Study the NC machining methods of digital gear tooth surface expressed by NURBS. First, derive the precise 3D coordinate of discrete point set of gear tooth surface through calculate, next, solve the processing parameters required for CNC machine tools for each point, last, get the exercise polynomial motion-functional of every axis by the method of curve fitting.